{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#使用双zeta基底进行Helium的HF计算，添加了中文注释并解释了一下代码参数，并把原作者恶趣味的命令行输入改成了直接调用\n",
    "\n",
    "基底：$\\boxed{R_{2s}(r)=C_1re^{-\\zeta_1r}+C_2re^{-\\zeta_2r}}$\n",
    "\n",
    "[源代码](https://github.com/prtkm/helium-hartree-fock/tree/master)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from itertools import product\n",
    "from scipy.linalg import eig\n",
    "\n",
    "\n",
    "def Suv(z1, z2):\n",
    "    ''' \n",
    "    返回重叠积分\n",
    "    '''\n",
    "    return (((z1 ** 3) * (z2 ** 3) / np.pi ** 2) ** 0.5) * 2 / (z1 + z2) ** 3 * 4 * np.pi \n",
    "\n",
    "def S_matrix(zetas, munus):\n",
    "    '''\n",
    "    返回重叠矩阵\n",
    "    '''\n",
    "    S = np.zeros((2,2))\n",
    "    \n",
    "    for mu, nu in munus:\n",
    "        S[mu - 1, nu - 1] =  Suv(zetas[mu], zetas[nu])\n",
    "\n",
    "    return S   \n",
    "\n",
    "\n",
    "def Tuv(z1, z2):\n",
    "    '''\n",
    "    返回动能积分\n",
    "    '''\n",
    "    return 4 * z1 * z2 * np.sqrt(z1 ** 3 * z2 ** 3 ) / (z1 + z2) ** 3 \n",
    "\n",
    "\n",
    "def Vuv(z1, z2):\n",
    "    '''\n",
    "    返回原子核吸引积分\n",
    "    '''\n",
    "    return - 8 * np.sqrt((z1 ** 3 * z2 ** 3)) / (z1 + z2) ** 2  \n",
    "\n",
    "\n",
    "def Huv(z1, z2):\n",
    "    '''\n",
    "    返回核哈密顿元素\n",
    "    '''\n",
    "    return Tuv(z1, z2) + Vuv(z1, z2)\n",
    "\n",
    "def H_matrix(zetas, munus):\n",
    "    '''\n",
    "    返回核哈密顿矩阵\n",
    "    '''\n",
    "    H = np.zeros((2,2))\n",
    "    \n",
    "    for mu, nu in munus:\n",
    "        H[mu - 1, nu - 1] =  Huv(zetas[mu], zetas[nu])\n",
    "\n",
    "    return H    \n",
    "\n",
    "def I_two_electron(z):\n",
    "    '''\n",
    "    计算双电子积分\n",
    "    Args: z = [z1, z2, z3, z4]\n",
    "    Returns: (z1 z2 | z3 z4)\n",
    "    '''\n",
    "    A = np.prod(z) ** 1.5\n",
    "    \n",
    "    u = z[0] + z[1]\n",
    "    v = z[2] + z[3]\n",
    "    \n",
    "    integral = 32 * A / u ** 2 * (1 / (u * v ** 2) - 1 / (u + v) ** 3 - 1 / u / (u + v) ** 2)\n",
    "    return integral\n",
    "\n",
    "\n",
    "def get_C21(z1, z2, k):\n",
    "\n",
    "    '''\n",
    "    计算 C21\n",
    "    '''\n",
    "\n",
    "    S12 = Suv(z1, z2)\n",
    "    C21 = (1 + k ** 2 + 2 * k * S12) ** -0.5\n",
    "    return C21\n",
    "    \n",
    "def density_matrix(z1, z2, k):\n",
    "    '''\n",
    "    返回密度矩阵\n",
    "    '''\n",
    "\n",
    "    C21 = get_C21(z1, z2, k)\n",
    "\n",
    "    P11 = 2 * C21 ** 2 * k ** 2\n",
    "    P12 = 2 * k * C21 ** 2 \n",
    "    P21 = P12\n",
    "    P22 = 2 * C21 ** 2    \n",
    "    P =  np.array([[P11, P12],\n",
    "                   [P21, P22]])\n",
    "    return P\n",
    "\n",
    "\n",
    "def G_matrix(zetas, k, munus, lambdasigmas):\n",
    "\n",
    "    '''\n",
    "    返回 G 矩阵\n",
    "    '''\n",
    "    \n",
    "    G = np.zeros((2,2))\n",
    "\n",
    "    P = density_matrix(zetas[1], zetas[2], k)\n",
    "                       \n",
    "    for mu, nu in munus:    \n",
    "\n",
    "        g = 0\n",
    "        for l, s in lambdasigmas:\n",
    "\n",
    "            int1 = I_two_electron((zetas[mu], zetas[nu], zetas[s], zetas[l]))\n",
    "            int2 = I_two_electron((zetas[mu] , zetas[l], zetas[s], zetas[nu]))\n",
    "  \n",
    "            g+= P[l - 1, s - 1] * (int1 - 0.5 * int2)\n",
    "\n",
    "        G[mu - 1, nu - 1] = g\n",
    "    return G\n",
    "\n",
    "\n",
    "def F_matrix(zetas, k, munus, lambdasigmas):\n",
    "    '''\n",
    "    返回 Fock 矩阵\n",
    "    '''\n",
    "    return H_matrix(zetas, munus) + G_matrix(zetas, k, munus, lambdasigmas)\n",
    "\n",
    "\n",
    "def secular_eqn(F, S):\n",
    "    '''\n",
    "    返回离散方程的特征值和特征向量\n",
    "    '''    \n",
    "    ei, C = eig(F, S)\n",
    "    return ei, C\n",
    "\n",
    "\n",
    "def get_E0(P, H, F, orb_nos):\n",
    "\n",
    "    '''\n",
    "    返回哈特里-福克能量\n",
    "    '''\n",
    "    \n",
    "    E0 =0\n",
    "    for mu in orb_nos:\n",
    "\n",
    "        for nu in orb_nos:\n",
    "            E0 += 0.5 * (P[mu -1, nu - 1] * (H[mu - 1, nu - 1] + F[mu - 1, nu - 1]))\n",
    "\n",
    "    return E0\n",
    "\n",
    "def calculate(z1, z2, k):\n",
    "    '''\n",
    "    计算 HF 能量、k、C11、C12\n",
    "    '''\n",
    "    \n",
    "    orb_nos = [1,2]\n",
    "\n",
    "    # 将 zetas 存储在字典中    \n",
    "    zetas = {1:z1, 2:z2}\n",
    "\n",
    "    # mu-nu 组合\n",
    "    munus = list(product(orb_nos,repeat=2))\n",
    "    \n",
    "    # lambda-sigma 组合\n",
    "    lambdasigmas =  list(product(orb_nos,repeat=2))\n",
    "    \n",
    "    # 计算重叠积分\n",
    "    S = S_matrix(zetas, munus)\n",
    "\n",
    "    # 计算核哈密顿\n",
    "    H = H_matrix(zetas, munus)\n",
    "    \n",
    "    # 计算密度矩阵\n",
    "    P = density_matrix(z1, z2, k)\n",
    "    \n",
    "    # 计算 Fock 矩阵\n",
    "    F = F_matrix(zetas, k, munus, lambdasigmas)\n",
    "\n",
    "    # 解离散方程\n",
    "    ei, C = secular_eqn(F, S)\n",
    "\n",
    "    # 获取 k\n",
    "    k = C[0, 0] / C[1, 0]\n",
    "\n",
    "    # 计算 HF 能量\n",
    "    E0 = get_E0(P, H, F, orb_nos)\n",
    "\n",
    "    return E0, k, C[0,0], C[1,0]\n",
    "     \n",
    "def main(z1,z2,k0,n):\n",
    "    '''\n",
    "    接受 zeta1、zeta2、k 和最大收敛步数作为输入，并在氦原子上执行 scf 计算。\n",
    "    '''\n",
    "\n",
    "    print('Helium Hartree Fock Calculation')\n",
    "    print('-----------------------------')\n",
    "\n",
    "    \n",
    "    k = k0\n",
    "    C21_0 = get_C21(z1, z2, k)    \n",
    "    C11_0 = k0 * C21_0\n",
    "    \n",
    "    print('-' * 20)\n",
    "    print('开始模拟')\n",
    "    print('-' * 20)\n",
    "    print('\\n初始参数:')\n",
    "    print('z1 = {0}, z2 = {1}, k = {2}\\n'.format(z1, z2, k0))\n",
    "\n",
    "    for i in range(n):\n",
    "\n",
    "        print('-' * 20)\n",
    "        print('进入第 {0} 次迭代'.format(i + 1))\n",
    "        print('-' * 20)\n",
    "\n",
    "        print('使用 k = {0}\\n'.format(k))\n",
    "\n",
    "        E0, k, C11, C21 = calculate(z1, z2, k)\n",
    "        \n",
    "    # 将最终的最优能量 E0 从 Hartree 转换为 eV\n",
    "        E0_ev = E0 * 27.211386245988\n",
    "\n",
    "        print('迭代结果:')\n",
    "        print('E0 = {E0}\\nk = {k}\\nC11 = {C11}\\nC21 ={C21}\\nE0_ev = {E0_ev}\\n'.format(**locals()))\n",
    "        print('收敛程度:')\n",
    "        print('dC11 = {0:1.5f}'.format(np.abs(C11 - C11_0)))\n",
    "        print('dC21 = {0:1.5f}\\n'.format(np.abs(C21 - C21_0)))\n",
    "\n",
    "        if (np.abs(C11 - C11_0) < 1e-6) and (np.abs(C21 - C21_0) < 1e-6):\n",
    "            print('\\n在 {0} 次迭代中达到所需精度。停止模拟。'.format(i+1))\n",
    "            print('-' * 20)\n",
    "            converged = True\n",
    "            break\n",
    "\n",
    "        else:\n",
    "            C11_0 = C11\n",
    "            C21_0 = C21\n",
    "            \n",
    "    return E0_ev\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861452968747674\n",
      "k = 4.685312912511029\n",
      "C11 = -0.9779729599145256\n",
      "C21 =-0.20873162116943741\n",
      "E0_ev = -77.86410195732198\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83077\n",
      "dC21 = 0.37929\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.685312912511029\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616720608512196\n",
      "k = 4.670623764503631\n",
      "C11 = -0.9778387705604802\n",
      "C21 =-0.2093593532392776\n",
      "E0_ev = -77.870063757175\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00013\n",
      "dC21 = 0.00063\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.670623764503631\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725964495706\n",
      "k = 4.669902557484073\n",
      "C11 = -0.9778321509377365\n",
      "C21 =-0.20939026861934076\n",
      "E0_ev = -77.87007833154861\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00003\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669902557484073\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977478525\n",
      "k = 4.669867061885926\n",
      "C11 = -0.9778318250644836\n",
      "C21 =-0.20939179040989367\n",
      "E0_ev = -77.87007836687667\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669867061885926\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977509985\n",
      "k = 4.669865314693536\n",
      "C11 = -0.9778318090239093\n",
      "C21 =-0.20939186531722928\n",
      "E0_ev = -77.87007836696226\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-77.87007836696226"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z1 = 1.45363\n",
    "z2 = 2.91093\n",
    "k0 = 5\n",
    "n = 20\n",
    "main(z1, z2, k0, n)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.308267, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8401614127960286\n",
      "k = 3.188432142650314\n",
      "C11 = -0.9541714797341667\n",
      "C21 =-0.29926040042396285\n",
      "E0_ev = -77.2847292045437\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.81273\n",
      "dC21 = 0.47097\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.188432142650314\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8559300347205188\n",
      "k = 3.1355064751059736\n",
      "C11 = -0.9527202310597921\n",
      "C21 =-0.3038489120095318\n",
      "E0_ev = -77.71381526629796\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00145\n",
      "dC21 = 0.00459\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.1355064751059736\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.85595894488501\n",
      "k = 3.1333650824903043\n",
      "C11 = -0.9526601035355937\n",
      "C21 =-0.3040373778527104\n",
      "E0_ev = -77.71460195195036\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00006\n",
      "dC21 = 0.00019\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.1333650824903043\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.855958993517627\n",
      "k = 3.1332774674160495\n",
      "C11 = -0.9526576410352466\n",
      "C21 =-0.304045093657436\n",
      "E0_ev = -77.71460327531129\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.1332774674160495\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8559589935991307\n",
      "k = 3.1332738810159158\n",
      "C11 = -0.9526575402322559\n",
      "C21 =-0.30404540950099496\n",
      "E0_ev = -77.71460327752911\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.3373396, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.847363957248661\n",
      "k = 3.4057306391249442\n",
      "C11 = -0.9594939441145327\n",
      "C21 =-0.2817292516007847\n",
      "E0_ev = -77.48072042359817\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.81681\n",
      "dC21 = 0.45319\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.4057306391249442\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8580672083253007\n",
      "k = 3.3547708156701983\n",
      "C11 = -0.9583304432020896\n",
      "C21 =-0.2856619709238288\n",
      "E0_ev = -77.7719707227324\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00116\n",
      "dC21 = 0.00393\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.3547708156701983\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8580883097765453\n",
      "k = 3.3526107126639637\n",
      "C11 = -0.9582800447613382\n",
      "C21 =-0.2858309916930066\n",
      "E0_ev = -77.77254492247258\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00005\n",
      "dC21 = 0.00017\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.3526107126639637\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.85808834864694\n",
      "k = 3.352518193330481\n",
      "C11 = -0.958277884148499\n",
      "C21 =-0.28583823528680696\n",
      "E0_ev = -77.7725459801899\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.352518193330481\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8580883487183235\n",
      "k = 3.3525142288824785\n",
      "C11 = -0.9582777915626955\n",
      "C21 =-0.2858385456822136\n",
      "E0_ev = -77.77254598213234\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.3664122, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8530687563965316\n",
      "k = 3.654770643414215\n",
      "C11 = -0.964546139967972\n",
      "C21 =-0.263914273719489\n",
      "E0_ev = -77.63595591666666\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82066\n",
      "dC21 = 0.43514\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.654770643414215\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8596818373858444\n",
      "k = 3.607705995315724\n",
      "C11 = -0.9636652112381041\n",
      "C21 =-0.26711301100736456\n",
      "E0_ev = -77.81590701774286\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00088\n",
      "dC21 = 0.00320\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.607705995315724\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.859695736777663\n",
      "k = 3.6056257165607017\n",
      "C11 = -0.9636255327057057\n",
      "C21 =-0.2672561182043263\n",
      "E0_ev = -77.81628523946222\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00004\n",
      "dC21 = 0.00014\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.6056257165607017\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8596957645297363\n",
      "k = 3.605532917323628\n",
      "C11 = -0.9636237611984182\n",
      "C21 =-0.26726250551436154\n",
      "E0_ev = -77.8162859946346\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.605532917323628\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.859695764585015\n",
      "k = 3.6055287759471617\n",
      "C11 = -0.963623682137926\n",
      "C21 =-0.26726279056940405\n",
      "E0_ev = -77.81628599613882\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.3954848000000002, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.857302259758876\n",
      "k = 3.9433457095536744\n",
      "C11 = -0.9693177752456871\n",
      "C21 =-0.24581100584138205\n",
      "E0_ev = -77.75115541183311\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82428\n",
      "dC21 = 0.41680\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.9433457095536744\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.86080292561012\n",
      "k = 3.902808068993391\n",
      "C11 = -0.9687068487056704\n",
      "C21 =-0.24820765755860458\n",
      "E0_ev = -77.84641338242945\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00061\n",
      "dC21 = 0.00240\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.902808068993391\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608107115120607\n",
      "k = 3.9009469105816557\n",
      "C11 = -0.9686783699860816\n",
      "C21 =-0.24831877802757524\n",
      "E0_ev = -77.84662524761443\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00003\n",
      "dC21 = 0.00011\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.9009469105816557\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608107282157267\n",
      "k = 3.9008608139853465\n",
      "C11 = -0.9686770516438594\n",
      "C21 =-0.24832392075384063\n",
      "E0_ev = -77.84662570214434\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.9008608139853465\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608107282515007\n",
      "k = 3.9008568297986415\n",
      "C11 = -0.9686769906345687\n",
      "C21 =-0.24832415874247066\n",
      "E0_ev = -77.8466257031178\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.4245574, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8600892560805784\n",
      "k = 4.281991576725018\n",
      "C11 = -0.9737974786031691\n",
      "C21 =-0.227416953339258\n",
      "E0_ev = -77.8269934452091\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82766\n",
      "dC21 = 0.39819\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.281991576725018\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861457766046478\n",
      "k = 4.251684673146432\n",
      "C11 = -0.9734373985830836\n",
      "C21 =-0.22895333812765978\n",
      "E0_ev = -77.86423249847267\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00036\n",
      "dC21 = 0.00154\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.251684673146432\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614609661499966\n",
      "k = 4.250243928964301\n",
      "C11 = -0.9734200989444703\n",
      "C21 =-0.22902687827182502\n",
      "E0_ev = -77.86431957772555\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00002\n",
      "dC21 = 0.00007\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.250243928964301\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861460973471522\n",
      "k = 4.250175072016837\n",
      "C11 = -0.9734192717318975\n",
      "C21 =-0.22903039409856132\n",
      "E0_ev = -77.8643197769544\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.250175072016837\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861460973488255\n",
      "k = 4.250171780326033\n",
      "C11 = -0.9734192321862334\n",
      "C21 =-0.2290305621744921\n",
      "E0_ev = -77.86431977740973\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861452968747674\n",
      "k = 4.685312912511029\n",
      "C11 = -0.9779729599145256\n",
      "C21 =-0.20873162116943741\n",
      "E0_ev = -77.86410195732198\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83077\n",
      "dC21 = 0.37929\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.685312912511029\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616720608512196\n",
      "k = 4.670623764503631\n",
      "C11 = -0.9778387705604802\n",
      "C21 =-0.2093593532392776\n",
      "E0_ev = -77.870063757175\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00013\n",
      "dC21 = 0.00063\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.670623764503631\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725964495706\n",
      "k = 4.669902557484073\n",
      "C11 = -0.9778321509377365\n",
      "C21 =-0.20939026861934076\n",
      "E0_ev = -77.87007833154861\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00003\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669902557484073\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977478525\n",
      "k = 4.669867061885926\n",
      "C11 = -0.9778318250644836\n",
      "C21 =-0.20939179040989367\n",
      "E0_ev = -77.87007836687667\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669867061885926\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977509985\n",
      "k = 4.669865314693536\n",
      "C11 = -0.9778318090239093\n",
      "C21 =-0.20939186531722928\n",
      "E0_ev = -77.87007836696226\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.4827026, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861415145736246\n",
      "k = 5.174162282045894\n",
      "C11 = -0.9818311731219017\n",
      "C21 =-0.18975654793990726\n",
      "E0_ev = -77.86307274074902\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83361\n",
      "dC21 = 0.36011\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.174162282045894\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614700308623453\n",
      "k = 5.183217852491688\n",
      "C11 = -0.9818928905919421\n",
      "C21 =-0.18943693252636956\n",
      "E0_ev = -77.86456624111447\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00006\n",
      "dC21 = 0.00032\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.183217852491688\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861470170432297\n",
      "k = 5.18367616531642\n",
      "C11 = -0.9818960058959662\n",
      "C21 =-0.1894207845130753\n",
      "E0_ev = -77.86457003900634\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00002\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.18367616531642\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614701707886847\n",
      "k = 5.18369932898939\n",
      "C11 = -0.9818961633259717\n",
      "C21 =-0.1894199684450837\n",
      "E0_ev = -77.86457004870415\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 4 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.5117752000000002, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8599961443544912\n",
      "k = 5.77938666575949\n",
      "C11 = -0.9853584828526272\n",
      "C21 =-0.17049533797253513\n",
      "E0_ev = -77.82445974606651\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83616\n",
      "dC21 = 0.34066\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.77938666575949\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.860874516072014\n",
      "k = 5.824976882461897\n",
      "C11 = -0.9855818614253362\n",
      "C21 =-0.16919927431691112\n",
      "E0_ev = -77.84836145813958\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00022\n",
      "dC21 = 0.00130\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.824976882461897\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608768292689697\n",
      "k = 5.827352356025649\n",
      "C11 = -0.9855933611565757\n",
      "C21 =-0.16913227499233746\n",
      "E0_ev = -77.8484244034354\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00007\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.827352356025649\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608768354598175\n",
      "k = 5.827475343065218\n",
      "C11 = -0.9855939561682191\n",
      "C21 =-0.16912880761324722\n",
      "E0_ev = -77.84842457189696\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 5.827475343065218\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8608768354764\n",
      "k = 5.827481708450126\n",
      "C11 = -0.9855939869629731\n",
      "C21 =-0.16912862815747923\n",
      "E0_ev = -77.84842457234818\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.5408478, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8572150110396\n",
      "k = 6.548636506538937\n",
      "C11 = -0.9885408357314898\n",
      "C21 =-0.15095368856469787\n",
      "E0_ev = -77.74878125323342\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83840\n",
      "dC21 = 0.32093\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 6.548636506538937\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8599070679364207\n",
      "k = 6.651942087441711\n",
      "C11 = -0.9888881324895045\n",
      "C21 =-0.14866156672597006\n",
      "E0_ev = -77.82203585324898\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00035\n",
      "dC21 = 0.00229\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 6.651942087441711\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8599143809254852\n",
      "k = 6.657481001751846\n",
      "C11 = -0.9889063081649628\n",
      "C21 =-0.14854061286915313\n",
      "E0_ev = -77.82223484981903\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00002\n",
      "dC21 = 0.00012\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 6.657481001751846\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.85991440134713\n",
      "k = 6.657774136937095\n",
      "C11 = -0.9889072688378516\n",
      "C21 =-0.14853421706684658\n",
      "E0_ev = -77.8222354055203\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 6.657774136937095\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8599144014042386\n",
      "k = 6.657789639730527\n",
      "C11 = -0.9889073196406939\n",
      "C21 =-0.14853387883260302\n",
      "E0_ev = -77.8222354070743\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.5699204, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.853089556469243\n",
      "k = 7.559618723095116\n",
      "C11 = -0.9913639368195998\n",
      "C21 =-0.13113940968886698\n",
      "E0_ev = -77.63652191547915\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.84032\n",
      "dC21 = 0.30093\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 7.559618723095116\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8585880343363095\n",
      "k = 7.758033550625281\n",
      "C11 = -0.991794677180703\n",
      "C21 =-0.12784098840366145\n",
      "E0_ev = -77.78614312048492\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00043\n",
      "dC21 = 0.00330\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 7.758033550625281\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.858603387089392\n",
      "k = 7.768987039380155\n",
      "C11 = -0.9918175152201772\n",
      "C21 =-0.12766368513588214\n",
      "E0_ev = -77.78656089017899\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00002\n",
      "dC21 = 0.00018\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 7.768987039380155\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8586034316451436\n",
      "k = 7.769578503587159\n",
      "C11 = -0.9918187457207298\n",
      "C21 =-0.12765412502915238\n",
      "E0_ev = -77.78656210260276\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 7.769578503587159\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.858603431774712\n",
      "k = 7.7696104028357516\n",
      "C11 = -0.9918188120770633\n",
      "C21 =-0.12765360946735108\n",
      "E0_ev = -77.78656210612849\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.598993, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.84763642624256\n",
      "k = 8.948241095996718\n",
      "C11 = -0.9938134311220409\n",
      "C21 =-0.11106243343919904\n",
      "E0_ev = -77.48813468263121\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.84191\n",
      "dC21 = 0.28068\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 8.948241095996718\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8569366378974923\n",
      "k = 9.31356339897275\n",
      "C11 = -0.9942851752495023\n",
      "C21 =-0.10675668728031293\n",
      "E0_ev = -77.74120633414302\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00047\n",
      "dC21 = 0.00431\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 9.31356339897275\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8569632438675234\n",
      "k = 9.334375730214346\n",
      "C11 = -0.9943104140492555\n",
      "C21 =-0.10652136176935564\n",
      "E0_ev = -77.74193031946999\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00003\n",
      "dC21 = 0.00024\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 9.334375730214346\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8569633238256724\n",
      "k = 9.335520608698538\n",
      "C11 = -0.9943117975854808\n",
      "C21 =-0.10650844653044984\n",
      "E0_ev = -77.74193249524205\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 9.335520608698538\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.856963324066593\n",
      "k = 9.33558346481076\n",
      "C11 = -0.9943118735298067\n",
      "C21 =-0.1065077375482457\n",
      "E0_ev = -77.74193250179785\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min Energy: (1.453630, -77.870078)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义 z2 和 z1s\n",
    "z2 = 2.91093\n",
    "z1s = np.linspace(1.45363*0.9, 1.45363*1.10, 11)\n",
    "\n",
    "energies = []\n",
    "\n",
    "for z1 in z1s:\n",
    "    E0 = main(z1, z2, 5, 20)\n",
    "    energies.append(E0)\n",
    "\n",
    "# 找到能量最低点的坐标\n",
    "min_idx = np.argmin(energies)\n",
    "min_z1 = z1s[min_idx]\n",
    "min_energy = energies[min_idx]\n",
    "\n",
    "# 绘制能量图\n",
    "plt.figure()\n",
    "plt.plot(z1s, energies, 'bo-', lw=2, ms=10)\n",
    "plt.xlabel('$\\zeta_{1}$', fontsize=24)\n",
    "plt.ylabel('Energy (eV)', fontsize=24)\n",
    "plt.ticklabel_format(useOffset=False)\n",
    "plt.tight_layout()\n",
    "plt.savefig('optimal-zeta-1.png')\n",
    "plt.show()\n",
    "min_idx = np.argmin(energies)\n",
    "min_z1 = z1s[min_idx]\n",
    "min_energy = energies[min_idx]\n",
    "\n",
    "print('Min Energy: ({:.6f}, {:.6f})'.format(min_z1, min_energy))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.619837, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8572019416419705\n",
      "k = 3.662472260138405\n",
      "C11 = -0.9646872944857058\n",
      "C21 =-0.2633978433052351\n",
      "E0_ev = -77.74842561680651\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.81231\n",
      "dC21 = 0.43292\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.662472260138405\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861034419929325\n",
      "k = 3.6052921124554818\n",
      "C11 = -0.9636191637192426\n",
      "C21 =-0.2672790813233005\n",
      "E0_ev = -77.85271266376309\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00107\n",
      "dC21 = 0.00388\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.6052921124554818\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861046403019715\n",
      "k = 3.6021697838981797\n",
      "C11 = -0.9635594742637376\n",
      "C21 =-0.26749418602390174\n",
      "E0_ev = -77.85303874026411\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00006\n",
      "dC21 = 0.00022\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.6021697838981797\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8610464397070148\n",
      "k = 3.6019972478984252\n",
      "C11 = -0.9635561716959798\n",
      "C21 =-0.26750608214877564\n",
      "E0_ev = -77.8530397385764\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.6019972478984252\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8610464398192033\n",
      "k = 3.6019877075380644\n",
      "C11 = -0.9635559890679796\n",
      "C21 =-0.2675067399734587\n",
      "E0_ev = -77.8530397416292\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.6780556, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8584951598383634\n",
      "k = 3.866340937886002\n",
      "C11 = -0.9681417980774272\n",
      "C21 =-0.2504025934678119\n",
      "E0_ev = -77.78361587664891\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.81679\n",
      "dC21 = 0.42013\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 3.866340937886002\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8612707215875095\n",
      "k = 3.81696130736546\n",
      "C11 = -0.9673523648290804\n",
      "C21 =-0.25343520327607555\n",
      "E0_ev = -77.85914275945451\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00079\n",
      "dC21 = 0.00303\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 3.81696130736546\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8612789485674903\n",
      "k = 3.814329355391098\n",
      "C11 = -0.9673094804350968\n",
      "C21 =-0.25359883489555524\n",
      "E0_ev = -77.85936662698441\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00004\n",
      "dC21 = 0.00016\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 3.814329355391098\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8612789724557928\n",
      "k = 3.8141876939830794\n",
      "C11 = -0.9673071698819931\n",
      "C21 =-0.25360764794242563\n",
      "E0_ev = -77.85936727701824\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 3.8141876939830794\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8612789725250782\n",
      "k = 3.8141800652491282\n",
      "C11 = -0.9673070454475159\n",
      "C21 =-0.2536081225584023\n",
      "E0_ev = -77.85936727890359\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.7362742, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.859570218112613\n",
      "k = 4.070373827818716\n",
      "C11 = -0.9711221034756738\n",
      "C21 =-0.2385830256765608\n",
      "E0_ev = -77.81286970258645\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82081\n",
      "dC21 = 0.40852\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.070373827818716\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861450128956412\n",
      "k = 4.0291465871520655\n",
      "C11 = -0.9705540892631093\n",
      "C21 =-0.2408832908581589\n",
      "E0_ev = -77.86402468266509\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00057\n",
      "dC21 = 0.00230\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.0291465871520655\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614554225210393\n",
      "k = 4.026998489483986\n",
      "C11 = -0.9705240422504379\n",
      "C21 =-0.24100432239665417\n",
      "E0_ev = -77.86416872789678\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00003\n",
      "dC21 = 0.00012\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.026998489483986\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861455437145415\n",
      "k = 4.026885692049202\n",
      "C11 = -0.970522463218531\n",
      "C21 =-0.24101068106670082\n",
      "E0_ev = -77.86416912584632\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.026885692049202\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614554371857754\n",
      "k = 4.026879766603797\n",
      "C11 = -0.9705223802657837\n",
      "C21 =-0.2410110151076862\n",
      "E0_ev = -77.86416912694459\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.7944928, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.860423680831423\n",
      "k = 4.274764435477665\n",
      "C11 = -0.9737122709436853\n",
      "C21 =-0.22778150366895764\n",
      "E0_ev = -77.83609360627456\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82443\n",
      "dC21 = 0.39793\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.274764435477665\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861575164230682\n",
      "k = 4.24203579904203\n",
      "C11 = -0.9733212215760102\n",
      "C21 =-0.2294467250360813\n",
      "E0_ev = -77.86742706580763\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00039\n",
      "dC21 = 0.00167\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.24203579904203\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861578251001979\n",
      "k = 4.240366346128006\n",
      "C11 = -0.9733010442926417\n",
      "C21 =-0.22953230094880583\n",
      "E0_ev = -77.86751106113364\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00002\n",
      "dC21 = 0.00009\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.240366346128006\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861578259141169\n",
      "k = 4.240280686113157\n",
      "C11 = -0.9733000083826002\n",
      "C21 =-0.22953669354251482\n",
      "E0_ev = -77.8675112826123\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.240280686113157\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8615782591626124\n",
      "k = 4.240276289553443\n",
      "C11 = -0.9732999552121938\n",
      "C21 =-0.22953691899984544\n",
      "E0_ev = -77.8675112831958\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.8527114, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8610522928056317\n",
      "k = 4.479689928625385\n",
      "C11 = -0.975978379754761\n",
      "C21 =-0.21786739602627914\n",
      "E0_ev = -77.8531990095036\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.82774\n",
      "dC21 = 0.38822\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.479689928625385\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616483215538424\n",
      "k = 4.455805874960361\n",
      "C11 = -0.9757294924722065\n",
      "C21 =-0.21897935409515268\n",
      "E0_ev = -77.86941777798486\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00025\n",
      "dC21 = 0.00111\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.455805874960361\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616498457924697\n",
      "k = 4.454611454906832\n",
      "C11 = -0.9757169456751602\n",
      "C21 =-0.21903525269311447\n",
      "E0_ev = -77.86945925463088\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00006\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.454611454906832\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861649849640243\n",
      "k = 4.454551477067176\n",
      "C11 = -0.9757163153839893\n",
      "C21 =-0.21903806037648246\n",
      "E0_ev = -77.86945935933413\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.454551477067176\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.86164984964995\n",
      "k = 4.454548464657815\n",
      "C11 = -0.975716283726741\n",
      "C21 =-0.21903820139527713\n",
      "E0_ev = -77.86945935959827\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.91093, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861452968747674\n",
      "k = 4.685312912511029\n",
      "C11 = -0.9779729599145256\n",
      "C21 =-0.20873162116943741\n",
      "E0_ev = -77.86410195732198\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83077\n",
      "dC21 = 0.37929\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.685312912511029\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616720608512196\n",
      "k = 4.670623764503631\n",
      "C11 = -0.9778387705604802\n",
      "C21 =-0.2093593532392776\n",
      "E0_ev = -77.870063757175\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00013\n",
      "dC21 = 0.00063\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.670623764503631\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725964495706\n",
      "k = 4.669902557484073\n",
      "C11 = -0.9778321509377365\n",
      "C21 =-0.20939026861934076\n",
      "E0_ev = -77.87007833154861\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00003\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669902557484073\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977478525\n",
      "k = 4.669867061885926\n",
      "C11 = -0.9778318250644836\n",
      "C21 =-0.20939179040989367\n",
      "E0_ev = -77.87007836687667\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 4.669867061885926\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616725977509985\n",
      "k = 4.669865314693536\n",
      "C11 = -0.9778318090239093\n",
      "C21 =-0.20939186531722928\n",
      "E0_ev = -77.87007836696226\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 2.9691486, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.86162278354452\n",
      "k = 4.891782977473346\n",
      "C11 = -0.9797382030374577\n",
      "C21 =-0.20028243434942858\n",
      "E0_ev = -77.86872285334924\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83358\n",
      "dC21 = 0.37105\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 4.891782977473346\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616488022888\n",
      "k = 4.886647255651777\n",
      "C11 = -0.9796968805034261\n",
      "C21 =-0.20048446905397818\n",
      "E0_ev = -77.86943085944948\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00004\n",
      "dC21 = 0.00020\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 4.886647255651777\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616488632136043\n",
      "k = 4.886399358132794\n",
      "C11 = -0.9796948827305868\n",
      "C21 =-0.2004942312175137\n",
      "E0_ev = -77.86943251729787\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 4.886399358132794\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8616488633558204\n",
      "k = 4.886387382584358\n",
      "C11 = -0.9796947862138593\n",
      "C21 =-0.20049470283621051\n",
      "E0_ev = -77.86943252116777\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 4 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 3.0273672, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861558963260863\n",
      "k = 5.099238052389306\n",
      "C11 = -0.9813083205255924\n",
      "C21 =-0.19244214732547918\n",
      "E0_ev = -77.86698621496033\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83619\n",
      "dC21 = 0.36342\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.099238052389306\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861580921331026\n",
      "k = 5.104025700317861\n",
      "C11 = -0.9813423953878078\n",
      "C21 =-0.19226830995907668\n",
      "E0_ev = -77.86758372448875\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00003\n",
      "dC21 = 0.00017\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.104025700317861\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.86158097067604\n",
      "k = 5.104253195239022\n",
      "C11 = -0.9813440122271575\n",
      "C21 =-0.19226005738557472\n",
      "E0_ev = -77.86758506723498\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00001\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.104253195239022\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861580970787268\n",
      "k = 5.10426399727191\n",
      "C11 = -0.9813440889935922\n",
      "C21 =-0.19225966554984106\n",
      "E0_ev = -77.86758507026165\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 4 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 3.0855858, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861258876798182\n",
      "k = 5.307805591940658\n",
      "C11 = -0.982711297498694\n",
      "C21 =-0.18514455370988667\n",
      "E0_ev = -77.85882044631711\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.83863\n",
      "dC21 = 0.35633\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.307805591940658\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861470744371637\n",
      "k = 5.3229006589169305\n",
      "C11 = -0.9828067047793974\n",
      "C21 =-0.1846374313097499\n",
      "E0_ev = -77.8645856566914\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00010\n",
      "dC21 = 0.00051\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.3229006589169305\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614712021711814\n",
      "k = 5.3236076445526805\n",
      "C11 = -0.9828111540238782\n",
      "C21 =-0.18461374685069593\n",
      "E0_ev = -77.86459811405163\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00002\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.3236076445526805\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614712031702765\n",
      "k = 5.323640683681103\n",
      "C11 = -0.9828113619058306\n",
      "C21 =-0.18461264016531118\n",
      "E0_ev = -77.86459814123839\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 5.323640683681103\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8614712031724583\n",
      "k = 5.32364222751928\n",
      "C11 = -0.9828113716195576\n",
      "C21 =-0.18461258845291142\n",
      "E0_ev = -77.86459814129776\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 3.1438044, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.86072002814466\n",
      "k = 5.517603621141727\n",
      "C11 = -0.9839702127091872\n",
      "C21 =-0.17833289236996328\n",
      "E0_ev = -77.844157627478\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.84092\n",
      "dC21 = 0.34972\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.517603621141727\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8613205449119388\n",
      "k = 5.543406475741906\n",
      "C11 = -0.9841155644305214\n",
      "C21 =-0.17752902817735577\n",
      "E0_ev = -77.86049852117962\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00015\n",
      "dC21 = 0.00080\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.543406475741906\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8613217948549634\n",
      "k = 5.544599063228088\n",
      "C11 = -0.9841222349961217\n",
      "C21 =-0.17749204654360737\n",
      "E0_ev = -77.86053253386204\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00004\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.544599063228088\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861321797502652\n",
      "k = 5.544653983930857\n",
      "C11 = -0.9841225420867249\n",
      "C21 =-0.17749034384090379\n",
      "E0_ev = -77.86053260590933\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 5.544653983930857\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861321797508265\n",
      "k = 5.544656512700016\n",
      "C11 = -0.9841225562261937\n",
      "C21 =-0.17749026544242452\n",
      "E0_ev = -77.86053260606207\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n",
      "Helium Hartree Fock Calculation\n",
      "-----------------------------\n",
      "--------------------\n",
      "开始模拟\n",
      "--------------------\n",
      "\n",
      "初始参数:\n",
      "z1 = 1.45363, z2 = 3.202023, k = 5\n",
      "\n",
      "--------------------\n",
      "进入第 1 次迭代\n",
      "--------------------\n",
      "使用 k = 5\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8599400491589466\n",
      "k = 5.728741656852604\n",
      "C11 = -0.985104242756743\n",
      "C21 =-0.17195822429492547\n",
      "E0_ev = -77.822933318034\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 1.84309\n",
      "dC21 = 0.34356\n",
      "\n",
      "--------------------\n",
      "进入第 2 次迭代\n",
      "--------------------\n",
      "使用 k = 5.728741656852604\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861132540260784\n",
      "k = 5.765670794970201\n",
      "C11 = -0.985290270350174\n",
      "C21 =-0.17088909606315225\n",
      "E0_ev = -77.855382654001\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00019\n",
      "dC21 = 0.00107\n",
      "\n",
      "--------------------\n",
      "进入第 3 次迭代\n",
      "--------------------\n",
      "使用 k = 5.765670794970201\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.8611349354334186\n",
      "k = 5.767357082278469\n",
      "C11 = -0.9852986821648436\n",
      "C21 =-0.17084058921761588\n",
      "E0_ev = -77.85544782996868\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00001\n",
      "dC21 = 0.00005\n",
      "\n",
      "--------------------\n",
      "进入第 4 次迭代\n",
      "--------------------\n",
      "使用 k = 5.767357082278469\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861134940369481\n",
      "k = 5.767433697951473\n",
      "C11 = -0.9852990641815901\n",
      "C21 =-0.17083838597599432\n",
      "E0_ev = -77.85544796428579\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "--------------------\n",
      "进入第 5 次迭代\n",
      "--------------------\n",
      "使用 k = 5.767433697951473\n",
      "\n",
      "迭代结果:\n",
      "E0 = -2.861134940379665\n",
      "k = 5.767437178154188\n",
      "C11 = -0.9852990815340295\n",
      "C21 =-0.17083828589691977\n",
      "E0_ev = -77.85544796456291\n",
      "\n",
      "收敛程度:\n",
      "dC11 = 0.00000\n",
      "dC21 = 0.00000\n",
      "\n",
      "\n",
      "在 5 次迭代中达到所需精度。停止模拟。\n",
      "--------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min Energy: (2.910930, -77.870078)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义 z1 和 z2s\n",
    "z1 = 1.45363\n",
    "z2s = np.linspace(2.91093*0.9, 2.91093*1.10, 11)\n",
    "\n",
    "energies = []\n",
    "\n",
    "for z2 in z2s:\n",
    "    E0 = main(z1, z2, 5, 20)\n",
    "    energies.append(E0)\n",
    "\n",
    "# 找到能量最低点的坐标\n",
    "min_idx = np.argmin(energies)\n",
    "min_z2 = z2s[min_idx]\n",
    "min_energy = energies[min_idx]\n",
    "\n",
    "# 绘制能量图\n",
    "plt.figure()\n",
    "plt.plot(z2s, energies, 'bo-', lw=2, ms=10)\n",
    "plt.xlabel('$\\zeta_{2}$', fontsize=24)\n",
    "plt.ylabel('Energy (eV)', fontsize=24)\n",
    "plt.ticklabel_format(useOffset=False)\n",
    "plt.tight_layout()\n",
    "plt.savefig('optimal-zeta-2.png')\n",
    "plt.show()\n",
    "min_idx = np.argmin(energies)\n",
    "min_z2 = z2s[min_idx]\n",
    "min_energy = energies[min_idx]\n",
    "\n",
    "print('Min Energy: ({:.6f}, {:.6f})'.format(min_z2, min_energy))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
